
theorem A6B6:
  for a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6 be Complex holds
  <*a1,a2,a3,a4,a5,a6*> + <*b1,b2,b3,b4,b5,b6*> =
    <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5,a6+b6*>
  proof
    let a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6 be Complex;
    A1: <*a1,a2,a3,a4,a5*> + <*b1,b2,b3,b4,b5*> =
      <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5*> by A5B5;
    <*a1,a2,a3,a4,a5,a6*> = <*a1,a2,a3,a4,a5*>^<*a6*> &
    <*b1,b2,b3,b4,b5,b6*> = <*b1,b2,b3,b4,b5*>^<*b6*> by AOFA_A00:def 4; then
    <*a1,a2,a3,a4,a5,a6*> + <*b1,b2,b3,b4,b5,b6*> =
      <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5*>^<*a6+b6*> by A1,FINSEQ_9:40
    .= <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5,a6+b6*> by  AOFA_A00:def 4;
    hence thesis;
  end;
